Frequently recurring upper respiratory infections can be caused by many factors that have nothing to do with orthodontic treatment or with having braces or aligners in the mouth. One possible link could be the so-called microbial count in the mouth. Having more bacteria in the mouth of a patient with braces can make the lining of the mouth and throat more susceptible to their effects. This applies to patients with braces or aligners and poor oral hygiene; it does not apply to all patients.
This answer is for general information. Your own case needs an examination by an orthodontist.